powered by
This function returns the Hilbert-Schmidt norm of the matrix \({\mathbf{x}}\).
hilbert.schmidt.norm(x)
A numeric value.
a numeric vector or matrix
Frederick Novomestky fnovomes@poly.edu
The formula used to compute the norm is \(\left\| {\bf{x}} \right\|_2\). This is merely the entrywise norm with exponent 2.
Bellman, R. (1987). Matrix Analysis, Second edition, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics.
Golub, G. H. and C. F. Van Loan (1996). Matrix Computations, Third Edition, The John Hopkins University Press.
Horn, R. A. and C. R. Johnson (1985). Matrix Analysis, Cambridge University Press.
entrywise.norm
A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE ) print( hilbert.schmidt.norm( A ) )
Run the code above in your browser using DataLab